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Leon Ehrenpreis: Some Old Souvenirs Read chapter Read first chapter

2012 | OriginalPaper | Chapter

On Two Lacunary Series and Modular Curves

Author : Ahmed Sebbar

Published in: The Mathematical Legacy of Leon Ehrenpreis

Publisher: Springer Milan

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Abstract

We study, from different points of view, the two series \(\chi_{+}(z)= \sum_{n\geq0} z^{2^{n}}\) and \(\chi_{-}(z)= \sum_{n\geq0}(-1)^{n} z^{2^{n}}\). We show that the first series is related to the Jacobi theta function and the second is related to the Dedekind eta function and to the modular curve X 0(14). We also present another approach to a celebrated identity of Hardy.

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previous chapter Bounded Cohomology for Solutions of Systems of Differential Equations: Applications to Extension Problems
next chapter PT Symmetry and Weyl Asymptotics
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Metadata
Title
On Two Lacunary Series and Modular Curves
Author
Ahmed Sebbar
Copyright Year
2012
Publisher
Springer Milan
Book
The Mathematical Legacy of Leon Ehrenpreis

Print ISBN: 978-88-470-1946-1

Electronic ISBN: 978-88-470-1947-8

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-88-470-1947-8_18

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